Question

a circle is inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the length of AD, BE and CF.

i need it real fast

Answer 1

Answer:

Let AD=x cm.

Here AD=AF,BD=BE,CE=CF [tangents to a point are equal]

So,AD=AF=x cm.

AB=AD+BD

12=x+BD

BD=12-x.

AC=AF+CF

10=x+CF

CF=10-x

BE=BD=12-x,CE=CF=10-x

BC=BE+CE

8=12-x+10-x

8=22-2x

2x=14

x=7 cm.

●AD=x=7 cm

●BE=12-7=5 cm

●CF=10-7=3 cm.

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